Nonlinear Partial Differential Equations And Their Numerical Computing

In this thesis,the main research is about nonlinear partial differential equations.As these equations originate from physics and other applied subjects,with obvious physical meaning,they are also called nonlinear mathematical physics equations.We mainly summarizes some classical nonlinear partial differential equations and their solitary wave solutions,especially emphasizes the inverse scattering transform method(IST).Using this method,we get the single soliton solution and multiple soliton solutions of KdV equation.IST is the most common method in solving nonlinear partial differential equations.We also consider a numerical method of nonlinear partial differential equations-------- Adomian decomposition method(ADM).The main points of the decomposition method is:the principle,the Adomian polynomials,the noise terms and the convergence results.This method is very easy and practical,but the disadvantage of this method is very obvious-----the convergent domain is very narrow.Using ADM,we get a series solution.In this paper,we used the Padéapproximant with ADM in overcoming this drawback.The ADM method together with Padéapproximant extends the domain of solution and gives better accuracy and better convergence than using ADM alone.